A decomposition method is usually defined by providing a tree whose nodes are the variables of the new problem; for each node, also provided are the associated set of original variables and possibly a set of original constraints used to build the domain of the variable in the new problem. Of the above three conditions (tree structure, enforcement of constraints, and equivalence of copies of original variables), the first one is automatically enforced by this definition. The condition of enforcement of constraints is in mostly formulated as: the scope of each constraint is a subset of the variables of some node; however, a different condition may be used when nodes are also associated to sets of constraints. The equivalence of all copies of the original variables is usually formulated as: the subgraph induced by the nodes associated to an original variable is connected.